A classification of structural dissipations for evolution operators |
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Authors: | M. D'Abbicco M.R. Ebert |
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Affiliation: | 1. Departamento de Computa??o e Matemática, Universidade de S?o Paulo (USP), FFCLRP, Av.Bandeirantes, 3900, Campus da USP, CEP 14040‐901, Ribeir?o Preto, SPBrazil;2. Departamento de Computa??o e Matemática, Universidade de S?o Paulo (USP), Ribeir?o Preto, SP, Brazil |
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Abstract: | In this paper, we study the asymptotic profile of the solution for a σ‐evolution equation with a time‐dependent structural damping. We introduce a classification of the damping term, which clarifies whether the solution behaves like the solution to an anomalous diffusion problem. We call this damping effective, whereas we say that the damping is noneffective when the solution shows oscillations in its asymptotic profile that cannot be neglected. Our classification shows a completely new interplay between the strength of the damping and the long time behavior of its coefficient. Copyright © 2015 John Wiley & Sons, Ltd. |
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Keywords: | evolution operators effective structural damping decay estimates diffusion phenomena 35L15 35B40 |
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